Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(919,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.919");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.p (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 919.4 | ||
Root | \(1.26359 - 0.635098i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.919 |
Dual form | 1638.2.p.i.991.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.97513 | − | 3.42102i | 0.883304 | − | 1.52993i | 0.0356582 | − | 0.999364i | \(-0.488647\pi\) |
0.847646 | − | 0.530563i | \(-0.178019\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.48662 | − | 2.18860i | −0.561891 | − | 0.827211i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.95025 | 1.24918 | ||||||||
\(11\) | −4.91377 | −1.48156 | −0.740779 | − | 0.671749i | \(-0.765544\pi\) | ||||
−0.740779 | + | 0.671749i | \(0.765544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.39335 | + | 1.21869i | −0.941145 | + | 0.338004i | ||||
\(14\) | 1.15207 | − | 2.38175i | 0.307903 | − | 0.636550i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.0702857 | − | 0.121738i | 0.0170468 | − | 0.0295259i | −0.857376 | − | 0.514690i | \(-0.827907\pi\) |
0.874423 | + | 0.485164i | \(0.161240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.776963 | −0.178248 | −0.0891238 | − | 0.996021i | \(-0.528407\pi\) | ||||
−0.0891238 | + | 0.996021i | \(0.528407\pi\) | |||||||
\(20\) | 1.97513 | + | 3.42102i | 0.441652 | + | 0.764963i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.45689 | − | 4.25545i | −0.523810 | − | 0.907266i | ||||
\(23\) | 4.76845 | + | 8.25920i | 0.994291 | + | 1.72216i | 0.589556 | + | 0.807728i | \(0.299303\pi\) |
0.404735 | + | 0.914434i | \(0.367364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.30226 | − | 9.18378i | −1.06045 | − | 1.83676i | ||||
\(26\) | −2.75209 | − | 2.32938i | −0.539729 | − | 0.456829i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.63869 | − | 0.193156i | 0.498666 | − | 0.0365030i | ||||
\(29\) | 0.629759 | − | 1.09077i | 0.116943 | − | 0.202552i | −0.801612 | − | 0.597845i | \(-0.796024\pi\) |
0.918555 | + | 0.395293i | \(0.129357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.67992 | − | 2.90971i | −0.301723 | − | 0.522600i | 0.674803 | − | 0.737998i | \(-0.264229\pi\) |
−0.976526 | + | 0.215398i | \(0.930895\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.140571 | 0.0241078 | ||||||||
\(35\) | −10.4235 | + | 0.763015i | −1.76189 | + | 0.128973i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.56841 | − | 9.64476i | −0.915440 | − | 1.58559i | −0.806256 | − | 0.591567i | \(-0.798509\pi\) |
−0.109185 | − | 0.994021i | \(-0.534824\pi\) | |||||||
\(38\) | −0.388481 | − | 0.672870i | −0.0630200 | − | 0.109154i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.97513 | + | 3.42102i | −0.312295 | + | 0.540911i | ||||
\(41\) | −4.65505 | + | 8.06279i | −0.726997 | + | 1.25920i | 0.231150 | + | 0.972918i | \(0.425751\pi\) |
−0.958147 | + | 0.286277i | \(0.907582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.541233 | − | 0.937443i | −0.0825372 | − | 0.142959i | 0.821802 | − | 0.569773i | \(-0.192969\pi\) |
−0.904339 | + | 0.426815i | \(0.859636\pi\) | |||||||
\(44\) | 2.45689 | − | 4.25545i | 0.370390 | − | 0.641534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.76845 | + | 8.25920i | −0.703070 | + | 1.21775i | ||||
\(47\) | −3.33199 | + | 5.77118i | −0.486021 | + | 0.841813i | −0.999871 | − | 0.0160671i | \(-0.994885\pi\) |
0.513850 | + | 0.857880i | \(0.328219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.57990 | + | 6.50724i | −0.368557 | + | 0.929605i | ||||
\(50\) | 5.30226 | − | 9.18378i | 0.749852 | − | 1.29878i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.641255 | − | 3.54807i | 0.0889261 | − | 0.492029i | ||||
\(53\) | −5.53204 | − | 9.58177i | −0.759884 | − | 1.31616i | −0.942910 | − | 0.333049i | \(-0.891923\pi\) |
0.183026 | − | 0.983108i | \(-0.441411\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.70533 | + | 16.8101i | −1.30867 | + | 2.26668i | ||||
\(56\) | 1.48662 | + | 2.18860i | 0.198658 | + | 0.292463i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.25952 | 0.165383 | ||||||||
\(59\) | 0.215609 | − | 0.373446i | 0.0280699 | − | 0.0486185i | −0.851649 | − | 0.524112i | \(-0.824397\pi\) |
0.879719 | + | 0.475494i | \(0.157731\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.28114 | −1.06029 | −0.530146 | − | 0.847906i | \(-0.677863\pi\) | ||||
−0.530146 | + | 0.847906i | \(0.677863\pi\) | |||||||
\(62\) | 1.67992 | − | 2.90971i | 0.213351 | − | 0.369534i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.53312 | + | 14.0158i | −0.314195 | + | 1.73844i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.19628 | 1.00134 | 0.500668 | − | 0.865640i | \(-0.333088\pi\) | ||||
0.500668 | + | 0.865640i | \(0.333088\pi\) | |||||||
\(68\) | 0.0702857 | + | 0.121738i | 0.00852340 | + | 0.0147630i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.87254 | − | 8.64551i | −0.701903 | − | 1.03334i | ||||
\(71\) | −1.93865 | − | 3.35783i | −0.230075 | − | 0.398502i | 0.727755 | − | 0.685837i | \(-0.240564\pi\) |
−0.957830 | + | 0.287336i | \(0.907230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0817820 | − | 0.141650i | −0.00957185 | − | 0.0165789i | 0.861200 | − | 0.508267i | \(-0.169714\pi\) |
−0.870772 | + | 0.491688i | \(0.836380\pi\) | |||||||
\(74\) | 5.56841 | − | 9.64476i | 0.647314 | − | 1.12118i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.388481 | − | 0.672870i | 0.0445619 | − | 0.0771834i | ||||
\(77\) | 7.30493 | + | 10.7543i | 0.832474 | + | 1.22556i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.17517 | − | 3.76751i | 0.244726 | − | 0.423878i | −0.717329 | − | 0.696735i | \(-0.754635\pi\) |
0.962055 | + | 0.272857i | \(0.0879687\pi\) | |||||||
\(80\) | −3.95025 | −0.441652 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.31010 | −1.02813 | ||||||||
\(83\) | 10.5220 | 1.15494 | 0.577472 | − | 0.816410i | \(-0.304039\pi\) | ||||
0.577472 | + | 0.816410i | \(0.304039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.277647 | − | 0.480898i | −0.0301150 | − | 0.0521607i | ||||
\(86\) | 0.541233 | − | 0.937443i | 0.0583626 | − | 0.101087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.91377 | 0.523810 | ||||||||
\(89\) | −0.536369 | − | 0.929018i | −0.0568550 | − | 0.0984757i | 0.836197 | − | 0.548429i | \(-0.184774\pi\) |
−0.893052 | + | 0.449953i | \(0.851441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.71185 | + | 5.61493i | 0.808421 | + | 0.588604i | ||||
\(92\) | −9.53690 | −0.994291 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.66398 | −0.687337 | ||||||||
\(95\) | −1.53460 | + | 2.65801i | −0.157447 | + | 0.272706i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.54097 | − | 11.3293i | −0.664135 | − | 1.15032i | −0.979519 | − | 0.201351i | \(-0.935467\pi\) |
0.315384 | − | 0.948964i | \(-0.397867\pi\) | |||||||
\(98\) | −6.92538 | + | 1.01936i | −0.699569 | + | 0.102971i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6045 | 1.06045 | ||||||||
\(101\) | −7.38523 | −0.734858 | −0.367429 | − | 0.930052i | \(-0.619762\pi\) | ||||
−0.367429 | + | 0.930052i | \(0.619762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.99107 | + | 3.44863i | −0.196186 | + | 0.339804i | −0.947289 | − | 0.320382i | \(-0.896189\pi\) |
0.751103 | + | 0.660185i | \(0.229522\pi\) | |||||||
\(104\) | 3.39335 | − | 1.21869i | 0.332745 | − | 0.119502i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.53204 | − | 9.58177i | 0.537319 | − | 0.930664i | ||||
\(107\) | −3.53679 | − | 6.12590i | −0.341914 | − | 0.592213i | 0.642874 | − | 0.765972i | \(-0.277742\pi\) |
−0.984788 | + | 0.173759i | \(0.944409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.42350 | − | 12.8579i | −0.711042 | − | 1.23156i | −0.964466 | − | 0.264206i | \(-0.914890\pi\) |
0.253424 | − | 0.967355i | \(-0.418443\pi\) | |||||||
\(110\) | −19.4107 | −1.85073 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.15207 | + | 2.38175i | −0.108860 | + | 0.225054i | ||||
\(113\) | 0.785895 | + | 1.36121i | 0.0739308 | + | 0.128052i | 0.900621 | − | 0.434606i | \(-0.143112\pi\) |
−0.826690 | + | 0.562658i | \(0.809779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37.6732 | 3.51304 | ||||||||
\(116\) | 0.629759 | + | 1.09077i | 0.0584717 | + | 0.101276i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.431218 | 0.0396969 | ||||||||
\(119\) | −0.370925 | + | 0.0271522i | −0.0340026 | + | 0.00248904i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1452 | 1.19502 | ||||||||
\(122\) | −4.14057 | − | 7.17168i | −0.374870 | − | 0.649293i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.35985 | 0.301723 | ||||||||
\(125\) | −22.1392 | −1.98019 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.42757 | + | 9.40083i | −0.481619 | + | 0.834188i | −0.999777 | − | 0.0210962i | \(-0.993284\pi\) |
0.518159 | + | 0.855285i | \(0.326618\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.4046 | + | 4.81414i | −1.17566 | + | 0.422228i | ||||
\(131\) | 0.961751 | − | 1.66580i | 0.0840285 | − | 0.145542i | −0.820948 | − | 0.571003i | \(-0.806555\pi\) |
0.904977 | + | 0.425461i | \(0.139888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.15505 | + | 1.70046i | 0.100156 | + | 0.147448i | ||||
\(134\) | 4.09814 | + | 7.09819i | 0.354026 | + | 0.613190i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0702857 | + | 0.121738i | −0.00602695 | + | 0.0104390i | ||||
\(137\) | 7.94106 | − | 13.7543i | 0.678450 | − | 1.17511i | −0.296997 | − | 0.954878i | \(-0.595985\pi\) |
0.975447 | − | 0.220232i | \(-0.0706815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.94351 | + | 5.09831i | 0.249665 | + | 0.432433i | 0.963433 | − | 0.267950i | \(-0.0863461\pi\) |
−0.713768 | + | 0.700383i | \(0.753013\pi\) | |||||||
\(140\) | 4.55096 | − | 9.40852i | 0.384626 | − | 0.795165i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.93865 | − | 3.35783i | 0.162688 | − | 0.281783i | ||||
\(143\) | 16.6741 | − | 5.98837i | 1.39436 | − | 0.500773i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48771 | − | 4.30884i | −0.206593 | − | 0.357829i | ||||
\(146\) | 0.0817820 | − | 0.141650i | 0.00676832 | − | 0.0117231i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.1368 | 0.915440 | ||||||||
\(149\) | 13.2701 | 1.08713 | 0.543564 | − | 0.839368i | \(-0.317075\pi\) | ||||
0.543564 | + | 0.839368i | \(0.317075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.06783 | − | 13.9739i | −0.656551 | − | 1.13718i | −0.981503 | − | 0.191449i | \(-0.938681\pi\) |
0.324952 | − | 0.945731i | \(-0.394652\pi\) | |||||||
\(152\) | 0.776963 | 0.0630200 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.66100 | + | 11.7034i | −0.456176 | + | 0.943086i | ||||
\(155\) | −13.2723 | −1.06605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.85322 | − | 15.3342i | −0.706564 | − | 1.22380i | −0.966124 | − | 0.258077i | \(-0.916911\pi\) |
0.259561 | − | 0.965727i | \(-0.416422\pi\) | |||||||
\(158\) | 4.35034 | 0.346095 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.97513 | − | 3.42102i | −0.156148 | − | 0.270455i | ||||
\(161\) | 10.9872 | − | 22.7145i | 0.865909 | − | 1.79016i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.27142 | 0.256237 | 0.128119 | − | 0.991759i | \(-0.459106\pi\) | ||||
0.128119 | + | 0.991759i | \(0.459106\pi\) | |||||||
\(164\) | −4.65505 | − | 8.06279i | −0.363498 | − | 0.629598i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26102 | + | 9.11236i | 0.408335 | + | 0.707256i | ||||
\(167\) | 4.42914 | − | 7.67150i | 0.342737 | − | 0.593638i | −0.642203 | − | 0.766535i | \(-0.721979\pi\) |
0.984940 | + | 0.172896i | \(0.0553126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0296 | − | 8.27088i | 0.771506 | − | 0.636221i | ||||
\(170\) | 0.277647 | − | 0.480898i | 0.0212945 | − | 0.0368832i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.08247 | 0.0825372 | ||||||||
\(173\) | 14.9497 | 1.13661 | 0.568303 | − | 0.822819i | \(-0.307600\pi\) | ||||
0.568303 | + | 0.822819i | \(0.307600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2171 | + | 25.2573i | −0.923527 | + | 1.90927i | ||||
\(176\) | 2.45689 | + | 4.25545i | 0.185195 | + | 0.320767i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.536369 | − | 0.929018i | 0.0402026 | − | 0.0696329i | ||||
\(179\) | 23.2069 | 1.73456 | 0.867281 | − | 0.497819i | \(-0.165866\pi\) | ||||
0.867281 | + | 0.497819i | \(0.165866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4618 | 1.44658 | 0.723291 | − | 0.690543i | \(-0.242629\pi\) | ||||
0.723291 | + | 0.690543i | \(0.242629\pi\) | |||||||
\(182\) | −1.00674 | + | 9.48612i | −0.0746248 | + | 0.703158i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.76845 | − | 8.25920i | −0.351535 | − | 0.608876i | ||||
\(185\) | −43.9932 | −3.23445 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.345368 | + | 0.598195i | −0.0252558 | + | 0.0437444i | ||||
\(188\) | −3.33199 | − | 5.77118i | −0.243010 | − | 0.420906i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.06920 | −0.222663 | ||||||||
\(191\) | 14.5964 | 1.05616 | 0.528078 | − | 0.849196i | \(-0.322913\pi\) | ||||
0.528078 | + | 0.849196i | \(0.322913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.76860 | −0.127307 | −0.0636534 | − | 0.997972i | \(-0.520275\pi\) | ||||
−0.0636534 | + | 0.997972i | \(0.520275\pi\) | |||||||
\(194\) | 6.54097 | − | 11.3293i | 0.469614 | − | 0.813396i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.34548 | − | 5.48788i | −0.310391 | − | 0.391991i | ||||
\(197\) | −2.92757 | + | 5.07070i | −0.208581 | + | 0.361272i | −0.951268 | − | 0.308366i | \(-0.900218\pi\) |
0.742687 | + | 0.669639i | \(0.233551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.96137 | + | 12.0575i | −0.493479 | + | 0.854730i | −0.999972 | − | 0.00751379i | \(-0.997608\pi\) |
0.506493 | + | 0.862244i | \(0.330942\pi\) | |||||||
\(200\) | 5.30226 | + | 9.18378i | 0.374926 | + | 0.649391i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.69262 | − | 6.39580i | −0.259812 | − | 0.450007i | ||||
\(203\) | −3.32348 | + | 0.243283i | −0.233262 | + | 0.0170751i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.3886 | + | 31.8501i | 1.28432 | + | 2.22450i | ||||
\(206\) | −3.98214 | −0.277449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.75209 | + | 2.32938i | 0.190823 | + | 0.161513i | ||||
\(209\) | 3.81782 | 0.264084 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.35399 | − | 5.80929i | 0.230898 | − | 0.399928i | −0.727174 | − | 0.686453i | \(-0.759167\pi\) |
0.958073 | + | 0.286525i | \(0.0925002\pi\) | |||||||
\(212\) | 11.0641 | 0.759884 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.53679 | − | 6.12590i | 0.241770 | − | 0.418758i | ||||
\(215\) | −4.27601 | −0.291622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.87077 | + | 8.00232i | −0.262765 | + | 0.543233i | ||||
\(218\) | 7.42350 | − | 12.8579i | 0.502783 | − | 0.870846i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.70533 | − | 16.8101i | −0.654333 | − | 1.13334i | ||||
\(221\) | −0.0901422 | + | 0.498757i | −0.00606362 | + | 0.0335500i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.02744 | + | 1.77957i | −0.0688023 | + | 0.119169i | −0.898374 | − | 0.439231i | \(-0.855251\pi\) |
0.829572 | + | 0.558400i | \(0.188584\pi\) | |||||||
\(224\) | −2.63869 | + | 0.193156i | −0.176305 | + | 0.0129058i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.785895 | + | 1.36121i | −0.0522770 | + | 0.0905463i | ||||
\(227\) | −12.9149 | + | 22.3692i | −0.857190 | + | 1.48470i | 0.0174074 | + | 0.999848i | \(0.494459\pi\) |
−0.874598 | + | 0.484849i | \(0.838875\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.39496 | − | 9.34435i | 0.356509 | − | 0.617492i | −0.630866 | − | 0.775892i | \(-0.717300\pi\) |
0.987375 | + | 0.158400i | \(0.0506336\pi\) | |||||||
\(230\) | 18.8366 | + | 32.6259i | 1.24205 | + | 2.15129i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.629759 | + | 1.09077i | −0.0413457 | + | 0.0716129i | ||||
\(233\) | 1.92109 | − | 3.32742i | 0.125855 | − | 0.217987i | −0.796212 | − | 0.605018i | \(-0.793166\pi\) |
0.922067 | + | 0.387031i | \(0.126499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.1622 | + | 22.7976i | 0.858608 | + | 1.48715i | ||||
\(236\) | 0.215609 | + | 0.373446i | 0.0140350 | + | 0.0243093i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.208977 | − | 0.307654i | −0.0135460 | − | 0.0199423i | ||||
\(239\) | −10.2560 | −0.663404 | −0.331702 | − | 0.943384i | \(-0.607623\pi\) | ||||
−0.331702 | + | 0.943384i | \(0.607623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.316427 | − | 0.548068i | 0.0203829 | − | 0.0353042i | −0.855654 | − | 0.517548i | \(-0.826845\pi\) |
0.876037 | + | 0.482244i | \(0.160178\pi\) | |||||||
\(242\) | 6.57259 | + | 11.3841i | 0.422502 | + | 0.731795i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.14057 | − | 7.17168i | 0.265073 | − | 0.459120i | ||||
\(245\) | 17.1658 | + | 21.6785i | 1.09668 | + | 1.38499i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.63650 | − | 0.946878i | 0.167757 | − | 0.0602484i | ||||
\(248\) | 1.67992 | + | 2.90971i | 0.106675 | + | 0.184767i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0696 | − | 19.1731i | −0.700104 | − | 1.21262i | ||||
\(251\) | −7.53648 | − | 13.0536i | −0.475698 | − | 0.823934i | 0.523914 | − | 0.851771i | \(-0.324471\pi\) |
−0.999612 | + | 0.0278373i | \(0.991138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.4311 | − | 40.5838i | −1.47310 | − | 2.55148i | ||||
\(254\) | −10.8551 | −0.681112 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.56909 | + | 9.64595i | 0.347390 | + | 0.601698i | 0.985785 | − | 0.168012i | \(-0.0537346\pi\) |
−0.638395 | + | 0.769709i | \(0.720401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8304 | + | 26.5251i | −0.797240 | + | 1.64819i | ||||
\(260\) | −10.8715 | − | 9.20163i | −0.674219 | − | 0.570661i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.92350 | 0.118834 | ||||||||
\(263\) | −17.1706 | −1.05878 | −0.529391 | − | 0.848378i | \(-0.677580\pi\) | ||||
−0.529391 | + | 0.848378i | \(0.677580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −43.7059 | −2.68483 | ||||||||
\(266\) | −0.895114 | + | 1.85053i | −0.0548829 | + | 0.113463i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.09814 | + | 7.09819i | −0.250334 | + | 0.433591i | ||||
\(269\) | 1.64355 | − | 2.84672i | 0.100209 | − | 0.173568i | −0.811562 | − | 0.584267i | \(-0.801382\pi\) |
0.911771 | + | 0.410699i | \(0.134715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.36304 | − | 12.7532i | −0.447273 | − | 0.774699i | 0.550935 | − | 0.834548i | \(-0.314271\pi\) |
−0.998207 | + | 0.0598494i | \(0.980938\pi\) | |||||||
\(272\) | −0.140571 | −0.00852340 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.8821 | 0.959474 | ||||||||
\(275\) | 26.0541 | + | 45.1270i | 1.57112 | + | 2.72126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.25021 | + | 16.0218i | −0.555791 | + | 0.962659i | 0.442050 | + | 0.896990i | \(0.354251\pi\) |
−0.997842 | + | 0.0656684i | \(0.979082\pi\) | |||||||
\(278\) | −2.94351 | + | 5.09831i | −0.176540 | + | 0.305776i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.4235 | − | 0.763015i | 0.622923 | − | 0.0455989i | ||||
\(281\) | 31.3463 | 1.86996 | 0.934981 | − | 0.354698i | \(-0.115416\pi\) | ||||
0.934981 | + | 0.354698i | \(0.115416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7197 | −0.874995 | −0.437498 | − | 0.899220i | \(-0.644135\pi\) | ||||
−0.437498 | + | 0.899220i | \(0.644135\pi\) | |||||||
\(284\) | 3.87729 | 0.230075 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.5231 | + | 11.4460i | 0.799640 | + | 0.676818i | ||||
\(287\) | 24.5665 | − | 1.79830i | 1.45011 | − | 0.106150i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.49012 | + | 14.7053i | 0.499419 | + | 0.865019i | ||||
\(290\) | 2.48771 | − | 4.30884i | 0.146083 | − | 0.253024i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.163564 | 0.00957185 | ||||||||
\(293\) | −8.39523 | − | 14.5410i | −0.490454 | − | 0.849492i | 0.509485 | − | 0.860479i | \(-0.329836\pi\) |
−0.999940 | + | 0.0109876i | \(0.996502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.851711 | − | 1.47521i | −0.0495886 | − | 0.0858899i | ||||
\(296\) | 5.56841 | + | 9.64476i | 0.323657 | + | 0.560590i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.63504 | + | 11.4922i | 0.384358 | + | 0.665727i | ||||
\(299\) | −26.2464 | − | 22.2150i | −1.51787 | − | 1.28473i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.24707 | + | 2.57816i | −0.0718801 | + | 0.148603i | ||||
\(302\) | 8.06783 | − | 13.9739i | 0.464252 | − | 0.804107i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.388481 | + | 0.672870i | 0.0222809 | + | 0.0385917i | ||||
\(305\) | −16.3563 | + | 28.3300i | −0.936560 | + | 1.62217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.69511 | 0.325037 | 0.162519 | − | 0.986705i | \(-0.448038\pi\) | ||||
0.162519 | + | 0.986705i | \(0.448038\pi\) | |||||||
\(308\) | −12.9659 | + | 0.949124i | −0.738802 | + | 0.0540814i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.63613 | − | 11.4941i | −0.376907 | − | 0.652822i | ||||
\(311\) | −0.183797 | − | 0.318345i | −0.0104221 | − | 0.0180517i | 0.860767 | − | 0.508999i | \(-0.169984\pi\) |
−0.871189 | + | 0.490947i | \(0.836651\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.95742 | + | 5.12240i | −0.167163 | + | 0.289535i | −0.937421 | − | 0.348197i | \(-0.886794\pi\) |
0.770258 | + | 0.637732i | \(0.220127\pi\) | |||||||
\(314\) | 8.85322 | − | 15.3342i | 0.499616 | − | 0.865360i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.17517 | + | 3.76751i | 0.122363 | + | 0.211939i | ||||
\(317\) | 4.28899 | − | 7.42875i | 0.240894 | − | 0.417240i | −0.720075 | − | 0.693896i | \(-0.755893\pi\) |
0.960969 | + | 0.276656i | \(0.0892262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.09449 | + | 5.35982i | −0.173258 | + | 0.300092i | ||||
\(320\) | 1.97513 | − | 3.42102i | 0.110413 | − | 0.191241i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.1649 | − | 1.84211i | 1.40239 | − | 0.102657i | ||||
\(323\) | −0.0546094 | + | 0.0945863i | −0.00303855 | + | 0.00526292i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.1846 | + | 24.7019i | 1.61887 | + | 1.37022i | ||||
\(326\) | 1.63571 | + | 2.83313i | 0.0905935 | + | 0.156912i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.65505 | − | 8.06279i | 0.257032 | − | 0.445193i | ||||
\(329\) | 17.5842 | − | 1.28719i | 0.969448 | − | 0.0709649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.14977 | −0.228092 | −0.114046 | − | 0.993475i | \(-0.536381\pi\) | ||||
−0.114046 | + | 0.993475i | \(0.536381\pi\) | |||||||
\(332\) | −5.26102 | + | 9.11236i | −0.288736 | + | 0.500106i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.85828 | 0.484704 | ||||||||
\(335\) | 16.1887 | − | 28.0397i | 0.884483 | − | 1.53197i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.5391 | 1.00989 | 0.504945 | − | 0.863152i | \(-0.331513\pi\) | ||||
0.504945 | + | 0.863152i | \(0.331513\pi\) | |||||||
\(338\) | 12.1776 | + | 4.55044i | 0.662373 | + | 0.247511i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.555293 | 0.0301150 | ||||||||
\(341\) | 8.25477 | + | 14.2977i | 0.447021 | + | 0.774262i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0770 | − | 4.02745i | 0.976069 | − | 0.217462i | ||||
\(344\) | 0.541233 | + | 0.937443i | 0.0291813 | + | 0.0505435i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.47486 | + | 12.9468i | 0.401851 | + | 0.696027i | ||||
\(347\) | −11.4934 | + | 19.9072i | −0.616999 | + | 1.06867i | 0.373032 | + | 0.927819i | \(0.378318\pi\) |
−0.990030 | + | 0.140854i | \(0.955015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.29494 | − | 12.6352i | 0.390489 | − | 0.676347i | −0.602025 | − | 0.798477i | \(-0.705639\pi\) |
0.992514 | + | 0.122130i | \(0.0389726\pi\) | |||||||
\(350\) | −27.9820 | + | 2.04832i | −1.49570 | + | 0.109487i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.45689 | + | 4.25545i | −0.130953 | + | 0.226816i | ||||
\(353\) | 19.7304 | 1.05015 | 0.525073 | − | 0.851057i | \(-0.324038\pi\) | ||||
0.525073 | + | 0.851057i | \(0.324038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.3163 | −0.812904 | ||||||||
\(356\) | 1.07274 | 0.0568550 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6034 | + | 20.0977i | 0.613260 | + | 1.06220i | ||||
\(359\) | −18.8344 | + | 32.6222i | −0.994044 | + | 1.72173i | −0.402644 | + | 0.915357i | \(0.631909\pi\) |
−0.591401 | + | 0.806378i | \(0.701425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3963 | −0.968228 | ||||||||
\(362\) | 9.73088 | + | 16.8544i | 0.511444 | + | 0.885847i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.71859 | + | 3.87119i | −0.456978 | + | 0.202906i | ||||
\(365\) | −0.646119 | −0.0338194 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50281 | 0.130646 | 0.0653229 | − | 0.997864i | \(-0.479192\pi\) | ||||
0.0653229 | + | 0.997864i | \(0.479192\pi\) | |||||||
\(368\) | 4.76845 | − | 8.25920i | 0.248573 | − | 0.430540i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.9966 | − | 38.0993i | −1.14355 | − | 1.98069i | ||||
\(371\) | −12.7466 | + | 26.3519i | −0.661768 | + | 1.36812i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.1674 | −0.681783 | −0.340891 | − | 0.940103i | \(-0.610729\pi\) | ||||
−0.340891 | + | 0.940103i | \(0.610729\pi\) | |||||||
\(374\) | −0.690736 | −0.0357171 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.33199 | − | 5.77118i | 0.171834 | − | 0.297626i | ||||
\(377\) | −0.807672 | + | 4.46886i | −0.0415972 | + | 0.230158i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.93228 | + | 10.2750i | −0.304721 | + | 0.527792i | −0.977199 | − | 0.212325i | \(-0.931896\pi\) |
0.672478 | + | 0.740117i | \(0.265230\pi\) | |||||||
\(380\) | −1.53460 | − | 2.65801i | −0.0787233 | − | 0.136353i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.29819 | + | 12.6408i | 0.373408 | + | 0.646761i | ||||
\(383\) | −16.4228 | −0.839165 | −0.419582 | − | 0.907717i | \(-0.637823\pi\) | ||||
−0.419582 | + | 0.907717i | \(0.637823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51.2187 | − | 3.74928i | 2.61035 | − | 0.191081i | ||||
\(386\) | −0.884301 | − | 1.53165i | −0.0450098 | − | 0.0779592i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.0819 | 0.664135 | ||||||||
\(389\) | −9.03721 | − | 15.6529i | −0.458205 | − | 0.793634i | 0.540662 | − | 0.841240i | \(-0.318174\pi\) |
−0.998866 | + | 0.0476065i | \(0.984841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.34062 | 0.0677979 | ||||||||
\(392\) | 2.57990 | − | 6.50724i | 0.130305 | − | 0.328665i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.85514 | −0.294978 | ||||||||
\(395\) | −8.59248 | − | 14.8826i | −0.432335 | − | 0.748826i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.40982 | −0.120945 | −0.0604726 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604726 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(398\) | −13.9227 | −0.697884 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.30226 | + | 9.18378i | −0.265113 | + | 0.459189i | ||||
\(401\) | −12.4622 | − | 21.5851i | −0.622331 | − | 1.07791i | −0.989051 | − | 0.147577i | \(-0.952852\pi\) |
0.366719 | − | 0.930332i | \(-0.380481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.24660 | + | 7.82635i | 0.460606 | + | 0.389858i | ||||
\(404\) | 3.69262 | − | 6.39580i | 0.183715 | − | 0.318203i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.87243 | − | 2.75658i | −0.0929271 | − | 0.136807i | ||||
\(407\) | 27.3619 | + | 47.3922i | 1.35628 | + | 2.34914i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7384 | + | 23.7957i | −0.679323 | + | 1.17662i | 0.295863 | + | 0.955231i | \(0.404393\pi\) |
−0.975185 | + | 0.221391i | \(0.928940\pi\) | |||||||
\(410\) | −18.3886 | + | 31.8501i | −0.908150 | + | 1.57296i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.99107 | − | 3.44863i | −0.0980929 | − | 0.169902i | ||||
\(413\) | −1.13785 | + | 0.0832924i | −0.0559901 | + | 0.00409855i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7824 | − | 35.9961i | 1.02017 | − | 1.76698i | ||||
\(416\) | −0.641255 | + | 3.54807i | −0.0314401 | + | 0.173958i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.90891 | + | 3.30633i | 0.0933678 | + | 0.161718i | ||||
\(419\) | 5.16655 | − | 8.94872i | 0.252402 | − | 0.437174i | −0.711784 | − | 0.702398i | \(-0.752113\pi\) |
0.964187 | + | 0.265224i | \(0.0854460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8702 | −0.822204 | −0.411102 | − | 0.911589i | \(-0.634856\pi\) | ||||
−0.411102 | + | 0.911589i | \(0.634856\pi\) | |||||||
\(422\) | 6.70799 | 0.326540 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.53204 | + | 9.58177i | 0.268659 | + | 0.465332i | ||||
\(425\) | −1.49069 | −0.0723092 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3109 | + | 18.1241i | 0.595768 | + | 0.877085i | ||||
\(428\) | 7.07358 | 0.341914 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.13801 | − | 3.70314i | −0.103104 | − | 0.178581i | ||||
\(431\) | −24.3436 | −1.17259 | −0.586294 | − | 0.810098i | \(-0.699414\pi\) | ||||
−0.586294 | + | 0.810098i | \(0.699414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.984059 | + | 1.70444i | 0.0472909 | + | 0.0819102i | 0.888702 | − | 0.458485i | \(-0.151608\pi\) |
−0.841411 | + | 0.540396i | \(0.818275\pi\) | |||||||
\(434\) | −8.86560 | + | 0.648974i | −0.425562 | + | 0.0311518i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.8470 | 0.711042 | ||||||||
\(437\) | −3.70491 | − | 6.41709i | −0.177230 | − | 0.306971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1318 | − | 17.5488i | −0.483564 | − | 0.837558i | 0.516258 | − | 0.856433i | \(-0.327325\pi\) |
−0.999822 | + | 0.0188756i | \(0.993991\pi\) | |||||||
\(440\) | 9.70533 | − | 16.8101i | 0.462683 | − | 0.801391i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.477008 | + | 0.171313i | −0.0226889 | + | 0.00814854i | ||||
\(443\) | 14.2707 | − | 24.7177i | 0.678024 | − | 1.17437i | −0.297551 | − | 0.954706i | \(-0.596170\pi\) |
0.975575 | − | 0.219666i | \(-0.0704967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.23759 | −0.200881 | ||||||||
\(446\) | −2.05487 | −0.0973011 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.48662 | − | 2.18860i | −0.0702364 | − | 0.103401i | ||||
\(449\) | −12.1517 | − | 21.0474i | −0.573475 | − | 0.993287i | −0.996206 | − | 0.0870320i | \(-0.972262\pi\) |
0.422731 | − | 0.906255i | \(-0.361072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.8739 | − | 39.6187i | 1.07709 | − | 1.86557i | ||||
\(452\) | −1.57179 | −0.0739308 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.8298 | −1.21225 | ||||||||
\(455\) | 34.4407 | − | 15.2922i | 1.61460 | − | 0.716909i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.12651 | + | 5.41528i | 0.146252 | + | 0.253316i | 0.929839 | − | 0.367966i | \(-0.119946\pi\) |
−0.783587 | + | 0.621282i | \(0.786612\pi\) | |||||||
\(458\) | 10.7899 | 0.504180 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.8366 | + | 32.6259i | −0.878261 | + | 1.52119i | ||||
\(461\) | −9.65625 | − | 16.7251i | −0.449736 | − | 0.778966i | 0.548632 | − | 0.836064i | \(-0.315149\pi\) |
−0.998369 | + | 0.0570976i | \(0.981815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4480 | 0.996772 | 0.498386 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498386 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(464\) | −1.25952 | −0.0584717 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.84218 | 0.177986 | ||||||||
\(467\) | −2.39255 | + | 4.14402i | −0.110714 | + | 0.191762i | −0.916058 | − | 0.401045i | \(-0.868647\pi\) |
0.805344 | + | 0.592807i | \(0.201980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1848 | − | 17.9384i | −0.562641 | − | 0.828316i | ||||
\(470\) | −13.1622 | + | 22.7976i | −0.607128 | + | 1.05158i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.215609 | + | 0.373446i | −0.00992422 | + | 0.0171893i | ||||
\(473\) | 2.65950 | + | 4.60638i | 0.122284 | + | 0.211802i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.11966 | + | 7.13545i | 0.189023 | + | 0.327397i | ||||
\(476\) | 0.161948 | − | 0.334806i | 0.00742287 | − | 0.0153458i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.12799 | − | 8.88194i | −0.234549 | − | 0.406250i | ||||
\(479\) | 11.7132 | 0.535190 | 0.267595 | − | 0.963532i | \(-0.413771\pi\) | ||||
0.267595 | + | 0.963532i | \(0.413771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.6495 | + | 25.9418i | 1.39750 | + | 1.18285i | ||||
\(482\) | 0.632854 | 0.0288257 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.57259 | + | 11.3841i | −0.298754 | + | 0.517457i | ||||
\(485\) | −51.6770 | −2.34653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8785 | − | 22.3062i | 0.583581 | − | 1.01079i | −0.411470 | − | 0.911423i | \(-0.634984\pi\) |
0.995051 | − | 0.0993684i | \(-0.0316822\pi\) | |||||||
\(488\) | 8.28114 | 0.374870 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.1913 | + | 25.7052i | −0.460395 | + | 1.16124i | ||||
\(491\) | −2.35012 | + | 4.07053i | −0.106059 | + | 0.183700i | −0.914171 | − | 0.405330i | \(-0.867157\pi\) |
0.808111 | + | 0.589030i | \(0.200490\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0885262 | − | 0.153332i | −0.00398702 | − | 0.00690572i | ||||
\(494\) | 2.13827 | + | 1.80984i | 0.0962054 | + | 0.0814285i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.67992 | + | 2.90971i | −0.0754308 | + | 0.130650i | ||||
\(497\) | −4.46690 | + | 9.23475i | −0.200368 | + | 0.414235i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3247 | − | 28.2752i | 0.730794 | − | 1.26577i | −0.225751 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941832\pi\) | |||||||
\(500\) | 11.0696 | − | 19.1731i | 0.495048 | − | 0.857449i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.53648 | − | 13.0536i | 0.336370 | − | 0.582609i | ||||
\(503\) | −7.49164 | − | 12.9759i | −0.334036 | − | 0.578567i | 0.649263 | − | 0.760564i | \(-0.275077\pi\) |
−0.983299 | + | 0.181997i | \(0.941744\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.5868 | + | 25.2650i | −0.649103 | + | 1.12428i | ||||
\(506\) | 23.4311 | − | 40.5838i | 1.04164 | − | 1.80417i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.42757 | − | 9.40083i | −0.240809 | − | 0.417094i | ||||
\(509\) | −0.210438 | − | 0.364489i | −0.00932749 | − | 0.0161557i | 0.861324 | − | 0.508056i | \(-0.169636\pi\) |
−0.870651 | + | 0.491900i | \(0.836302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.188437 | + | 0.389569i | −0.00833595 | + | 0.0172335i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.56909 | + | 9.64595i | −0.245642 | + | 0.425464i | ||||
\(515\) | 7.86522 | + | 13.6230i | 0.346583 | + | 0.600300i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3727 | − | 28.3583i | 0.720068 | − | 1.24720i | ||||
\(518\) | −29.3866 | + | 2.15114i | −1.29117 | + | 0.0945157i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.53312 | − | 14.0158i | 0.111085 | − | 0.614632i | ||||
\(521\) | 15.5914 | + | 27.0050i | 0.683070 | + | 1.18311i | 0.974039 | + | 0.226379i | \(0.0726888\pi\) |
−0.290969 | + | 0.956732i | \(0.593978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.18192 | − | 12.4394i | −0.314043 | − | 0.543939i | 0.665190 | − | 0.746674i | \(-0.268350\pi\) |
−0.979234 | + | 0.202735i | \(0.935017\pi\) | |||||||
\(524\) | 0.961751 | + | 1.66580i | 0.0420143 | + | 0.0727709i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.58528 | − | 14.8701i | −0.374336 | − | 0.648369i | ||||
\(527\) | −0.472299 | −0.0205737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33.9762 | + | 58.8486i | −1.47723 | + | 2.55863i | ||||
\(530\) | −21.8530 | − | 37.8504i | −0.949232 | − | 1.64412i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.05016 | + | 0.150075i | −0.0888859 | + | 0.00650657i | ||||
\(533\) | 5.97015 | − | 33.0329i | 0.258596 | − | 1.43081i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.9424 | −1.20806 | ||||||||
\(536\) | −8.19628 | −0.354026 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.28711 | 0.141717 | ||||||||
\(539\) | 12.6771 | − | 31.9751i | 0.546039 | − | 1.37726i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.68698 | − | 8.11808i | 0.201509 | − | 0.349024i | −0.747506 | − | 0.664255i | \(-0.768749\pi\) |
0.949015 | + | 0.315232i | \(0.102082\pi\) | |||||||
\(542\) | 7.36304 | − | 12.7532i | 0.316270 | − | 0.547795i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0702857 | − | 0.121738i | −0.00301348 | − | 0.00521949i | ||||
\(545\) | −58.6494 | −2.51227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7829 | 0.760343 | 0.380172 | − | 0.924916i | \(-0.375865\pi\) | ||||
0.380172 | + | 0.924916i | \(0.375865\pi\) | |||||||
\(548\) | 7.94106 | + | 13.7543i | 0.339225 | + | 0.587555i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.0541 | + | 45.1270i | −1.11095 | + | 1.92422i | ||||
\(551\) | −0.489299 | + | 0.847491i | −0.0208449 | + | 0.0361043i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4792 | + | 0.840294i | −0.488146 | + | 0.0357329i | ||||
\(554\) | −18.5004 | −0.786008 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.88702 | −0.249665 | ||||||||
\(557\) | −13.3641 | −0.566257 | −0.283128 | − | 0.959082i | \(-0.591372\pi\) | ||||
−0.283128 | + | 0.959082i | \(0.591372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.97904 | + | 2.52147i | 0.126000 | + | 0.106647i | ||||
\(560\) | 5.87254 | + | 8.64551i | 0.248160 | + | 0.365339i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6731 | + | 27.1467i | 0.661131 | + | 1.14511i | ||||
\(563\) | −13.6941 | + | 23.7189i | −0.577139 | + | 0.999634i | 0.418666 | + | 0.908140i | \(0.362498\pi\) |
−0.995806 | + | 0.0914943i | \(0.970836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.20897 | 0.261213 | ||||||||
\(566\) | −7.35985 | − | 12.7476i | −0.309357 | − | 0.535823i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.93865 | + | 3.35783i | 0.0813438 | + | 0.140892i | ||||
\(569\) | −5.48808 | − | 9.50564i | −0.230072 | − | 0.398497i | 0.727757 | − | 0.685835i | \(-0.240563\pi\) |
−0.957829 | + | 0.287338i | \(0.907230\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5552 | − | 25.2103i | −0.609115 | − | 1.05502i | −0.991387 | − | 0.130969i | \(-0.958191\pi\) |
0.382271 | − | 0.924050i | \(-0.375142\pi\) | |||||||
\(572\) | −3.15098 | + | 17.4344i | −0.131749 | + | 0.728969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.8406 | + | 20.3760i | 0.577696 | + | 0.850480i | ||||
\(575\) | 50.5671 | − | 87.5847i | 2.10879 | − | 3.65254i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0317 | − | 17.3753i | −0.417623 | − | 0.723345i | 0.578076 | − | 0.815983i | \(-0.303804\pi\) |
−0.995700 | + | 0.0926375i | \(0.970470\pi\) | |||||||
\(578\) | −8.49012 | + | 14.7053i | −0.353142 | + | 0.611661i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.97542 | 0.206593 | ||||||||
\(581\) | −15.6423 | − | 23.0285i | −0.648953 | − | 0.955383i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.1832 | + | 47.0826i | 1.12581 | + | 1.94996i | ||||
\(584\) | 0.0817820 | + | 0.141650i | 0.00338416 | + | 0.00586154i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.39523 | − | 14.5410i | 0.346804 | − | 0.600681i | ||||
\(587\) | −16.0113 | + | 27.7323i | −0.660855 | + | 1.14463i | 0.319536 | + | 0.947574i | \(0.396473\pi\) |
−0.980391 | + | 0.197060i | \(0.936860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.30524 | + | 2.26074i | 0.0537814 | + | 0.0931521i | ||||
\(590\) | 0.851711 | − | 1.47521i | 0.0350644 | − | 0.0607333i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.56841 | + | 9.64476i | −0.228860 | + | 0.396397i | ||||
\(593\) | −12.2192 | + | 21.1643i | −0.501784 | + | 0.869115i | 0.498214 | + | 0.867054i | \(0.333989\pi\) |
−0.999998 | + | 0.00206106i | \(0.999344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.639735 | + | 1.32257i | −0.0262266 | + | 0.0542201i | ||||
\(596\) | −6.63504 | + | 11.4922i | −0.271782 | + | 0.470740i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.11559 | − | 33.8376i | 0.250085 | − | 1.38372i | ||||
\(599\) | 7.93636 | + | 13.7462i | 0.324271 | + | 0.561654i | 0.981365 | − | 0.192155i | \(-0.0615477\pi\) |
−0.657093 | + | 0.753809i | \(0.728214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0246085 | + | 0.0426231i | −0.00100380 | + | 0.00173863i | −0.866527 | − | 0.499130i | \(-0.833653\pi\) |
0.865523 | + | 0.500869i | \(0.166986\pi\) | |||||||
\(602\) | −2.85629 | + | 0.209085i | −0.116414 | + | 0.00852165i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.1357 | 0.656551 | ||||||||
\(605\) | 25.9634 | − | 44.9699i | 1.05556 | − | 1.82829i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2265 | 0.536847 | 0.268423 | − | 0.963301i | \(-0.413497\pi\) | ||||
0.268423 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(608\) | −0.388481 | + | 0.672870i | −0.0157550 | + | 0.0272885i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.7126 | −1.32450 | ||||||||
\(611\) | 4.27331 | − | 23.6443i | 0.172880 | − | 0.956545i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.35096 | −0.0949543 | −0.0474772 | − | 0.998872i | \(-0.515118\pi\) | ||||
−0.0474772 | + | 0.998872i | \(0.515118\pi\) | |||||||
\(614\) | 2.84756 | + | 4.93211i | 0.114918 | + | 0.199044i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.30493 | − | 10.7543i | −0.294324 | − | 0.433302i | ||||
\(617\) | 16.1133 | + | 27.9090i | 0.648697 | + | 1.12358i | 0.983434 | + | 0.181264i | \(0.0580189\pi\) |
−0.334738 | + | 0.942311i | \(0.608648\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.49745 | + | 16.4501i | 0.381735 | + | 0.661184i | 0.991310 | − | 0.131544i | \(-0.0419934\pi\) |
−0.609575 | + | 0.792728i | \(0.708660\pi\) | |||||||
\(620\) | 6.63613 | − | 11.4941i | 0.266513 | − | 0.461615i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.183797 | − | 0.318345i | 0.00736957 | − | 0.0127645i | ||||
\(623\) | −1.23587 | + | 2.55500i | −0.0495140 | + | 0.102364i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2165 | + | 29.8199i | −0.688662 | + | 1.19280i | ||||
\(626\) | −5.91484 | −0.236404 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.7064 | 0.706564 | ||||||||
\(629\) | −1.56552 | −0.0624213 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7271 | − | 20.3119i | −0.466849 | − | 0.808606i | 0.532434 | − | 0.846471i | \(-0.321277\pi\) |
−0.999283 | + | 0.0378658i | \(0.987944\pi\) | |||||||
\(632\) | −2.17517 | + | 3.76751i | −0.0865237 | + | 0.149863i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.57798 | 0.340675 | ||||||||
\(635\) | 21.4403 | + | 37.1357i | 0.850832 | + | 1.47368i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.824188 | − | 25.2254i | 0.0326555 | − | 0.999467i | ||||
\(638\) | −6.18899 | −0.245024 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.95025 | 0.156148 | ||||||||
\(641\) | 2.80221 | − | 4.85357i | 0.110681 | − | 0.191705i | −0.805364 | − | 0.592780i | \(-0.798030\pi\) |
0.916045 | + | 0.401076i | \(0.131364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5626 | + | 20.0270i | 0.455983 | + | 0.789786i | 0.998744 | − | 0.0501012i | \(-0.0159544\pi\) |
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(644\) | 14.1778 | + | 20.8724i | 0.558683 | + | 0.822488i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.109219 | −0.00429716 | ||||||||
\(647\) | −17.7756 | −0.698832 | −0.349416 | − | 0.936968i | \(-0.613620\pi\) | ||||
−0.349416 | + | 0.936968i | \(0.613620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05945 | + | 1.83503i | −0.0415872 | + | 0.0720312i | ||||
\(650\) | −6.80020 | + | 37.6255i | −0.266726 | + | 1.47579i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.63571 | + | 2.83313i | −0.0640593 | + | 0.110954i | ||||
\(653\) | 1.25251 | + | 2.16941i | 0.0490145 | + | 0.0848956i | 0.889492 | − | 0.456951i | \(-0.151059\pi\) |
−0.840477 | + | 0.541847i | \(0.817725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.79916 | − | 6.58034i | −0.148445 | − | 0.257115i | ||||
\(656\) | 9.31010 | 0.363498 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.90683 | + | 14.5848i | 0.386209 | + | 0.568573i | ||||
\(659\) | 15.8598 | + | 27.4700i | 0.617810 | + | 1.07008i | 0.989884 | + | 0.141876i | \(0.0453134\pi\) |
−0.372074 | + | 0.928203i | \(0.621353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7146 | 0.883494 | 0.441747 | − | 0.897140i | \(-0.354359\pi\) | ||||
0.441747 | + | 0.897140i | \(0.354359\pi\) | |||||||
\(662\) | −2.07489 | − | 3.59381i | −0.0806427 | − | 0.139677i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5220 | −0.408335 | ||||||||
\(665\) | 8.09867 | − | 0.592834i | 0.314053 | − | 0.0229891i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0119 | 0.465103 | ||||||||
\(668\) | 4.42914 | + | 7.67150i | 0.171369 | + | 0.296819i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.3774 | 1.25085 | ||||||||
\(671\) | 40.6917 | 1.57088 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.56027 | + | 4.43452i | −0.0986911 | + | 0.170938i | −0.911143 | − | 0.412090i | \(-0.864799\pi\) |
0.812452 | + | 0.583028i | \(0.198132\pi\) | |||||||
\(674\) | 9.26955 | + | 16.0553i | 0.357050 | + | 0.618428i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.14800 | + | 12.8213i | 0.0826154 | + | 0.493127i | ||||
\(677\) | −1.02921 | + | 1.78264i | −0.0395556 | + | 0.0685123i | −0.885125 | − | 0.465353i | \(-0.845928\pi\) |
0.845570 | + | 0.533865i | \(0.179261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0713 | + | 31.1579i | −0.578383 | + | 1.19573i | ||||
\(680\) | 0.277647 | + | 0.480898i | 0.0106473 | + | 0.0184416i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.25477 | + | 14.2977i | −0.316091 | + | 0.547486i | ||||
\(683\) | −13.4644 | + | 23.3211i | −0.515202 | + | 0.892356i | 0.484642 | + | 0.874712i | \(0.338950\pi\) |
−0.999844 | + | 0.0176436i | \(0.994384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.3692 | − | 54.3330i | −1.19856 | − | 2.07596i | ||||
\(686\) | 12.5264 | + | 13.6415i | 0.478260 | + | 0.520833i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.541233 | + | 0.937443i | −0.0206343 | + | 0.0357397i | ||||
\(689\) | 30.4493 | + | 25.7724i | 1.16003 | + | 0.981850i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.6380 | − | 44.4064i | −0.975316 | − | 1.68930i | −0.678887 | − | 0.734243i | \(-0.737537\pi\) |
−0.296430 | − | 0.955055i | \(-0.595796\pi\) | |||||||
\(692\) | −7.47486 | + | 12.9468i | −0.284152 | + | 0.492165i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.9868 | −0.872568 | ||||||||
\(695\) | 23.2552 | 0.882121 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.654367 | + | 1.13340i | 0.0247859 | + | 0.0429305i | ||||
\(698\) | 14.5899 | 0.552235 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.7649 | − | 23.2090i | −0.595858 | − | 0.877217i | ||||
\(701\) | 26.2809 | 0.992617 | 0.496308 | − | 0.868146i | \(-0.334689\pi\) | ||||
0.496308 | + | 0.868146i | \(0.334689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.32644 | + | 7.49362i | 0.163175 | + | 0.282627i | ||||
\(704\) | −4.91377 | −0.185195 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.86522 | + | 17.0871i | 0.371283 | + | 0.643080i | ||||
\(707\) | 10.9791 | + | 16.1633i | 0.412910 | + | 0.607883i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.75932 | 0.328963 | 0.164482 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164482 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(710\) | −7.65815 | − | 13.2643i | −0.287405 | − | 0.497800i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.536369 | + | 0.929018i | 0.0201013 | + | 0.0348164i | ||||
\(713\) | 16.0213 | − | 27.7496i | 0.600001 | − | 1.03923i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.4472 | − | 68.8703i | 0.465498 | − | 2.57560i | ||||
\(716\) | −11.6034 | + | 20.0977i | −0.433640 | + | 0.751087i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −37.6689 | −1.40579 | ||||||||
\(719\) | 2.27601 | 0.0848810 | 0.0424405 | − | 0.999099i | \(-0.486487\pi\) | ||||
0.0424405 | + | 0.999099i | \(0.486487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5076 | − | 0.769173i | 0.391324 | − | 0.0286455i | ||||
\(722\) | −9.19816 | − | 15.9317i | −0.342320 | − | 0.592916i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.73088 | + | 16.8544i | −0.361645 | + | 0.626388i | ||||
\(725\) | −13.3566 | −0.496051 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.8719 | −1.47877 | −0.739383 | − | 0.673285i | \(-0.764883\pi\) | ||||
−0.739383 | + | 0.673285i | \(0.764883\pi\) | |||||||
\(728\) | −7.71185 | − | 5.61493i | −0.285820 | − | 0.208103i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.323060 | − | 0.559556i | −0.0119570 | − | 0.0207101i | ||||
\(731\) | −0.152164 | −0.00562798 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8845 | + | 22.3167i | −0.475901 | + | 0.824284i | −0.999619 | − | 0.0276073i | \(-0.991211\pi\) |
0.523718 | + | 0.851892i | \(0.324545\pi\) | |||||||
\(734\) | 1.25141 | + | 2.16750i | 0.0461903 | + | 0.0800039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.53690 | 0.351535 | ||||||||
\(737\) | −40.2747 | −1.48354 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8179 | 0.471512 | 0.235756 | − | 0.971812i | \(-0.424243\pi\) | ||||
0.235756 | + | 0.971812i | \(0.424243\pi\) | |||||||
\(740\) | 21.9966 | − | 38.0993i | 0.808612 | − | 1.40056i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −29.1947 | + | 2.13709i | −1.07177 | + | 0.0784551i | ||||
\(743\) | 10.1715 | − | 17.6176i | 0.373156 | − | 0.646326i | −0.616893 | − | 0.787047i | \(-0.711609\pi\) |
0.990049 | + | 0.140721i | \(0.0449422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.2101 | − | 45.3972i | 0.960264 | − | 1.66323i | ||||
\(746\) | −6.58371 | − | 11.4033i | −0.241047 | − | 0.417505i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.345368 | − | 0.598195i | −0.0126279 | − | 0.0218722i | ||||
\(749\) | −8.14924 | + | 16.8475i | −0.297767 | + | 0.615594i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2371 | + | 26.3914i | 0.556008 | + | 0.963034i | 0.997824 | + | 0.0659287i | \(0.0210010\pi\) |
−0.441816 | + | 0.897106i | \(0.645666\pi\) | |||||||
\(752\) | 6.66398 | 0.243010 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.27398 | + | 1.53496i | −0.155649 | + | 0.0559001i | ||||
\(755\) | −63.7400 | −2.31974 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7264 | − | 18.5787i | 0.389859 | − | 0.675256i | −0.602571 | − | 0.798065i | \(-0.705857\pi\) |
0.992430 | + | 0.122809i | \(0.0391904\pi\) | |||||||
\(758\) | −11.8646 | −0.430940 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.53460 | − | 2.65801i | 0.0556658 | − | 0.0964160i | ||||
\(761\) | 50.0476 | 1.81422 | 0.907112 | − | 0.420890i | \(-0.138282\pi\) | ||||
0.907112 | + | 0.420890i | \(0.138282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.1048 | + | 35.3619i | −0.619234 | + | 1.28019i | ||||
\(764\) | −7.29819 | + | 12.6408i | −0.264039 | + | 0.457329i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.21139 | − | 14.2225i | −0.296690 | − | 0.513881i | ||||
\(767\) | −0.276521 | + | 1.52999i | −0.00998460 | + | 0.0552448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.3820 | − | 43.9629i | 0.915298 | − | 1.58534i | 0.108833 | − | 0.994060i | \(-0.465289\pi\) |
0.806465 | − | 0.591282i | \(-0.201378\pi\) | |||||||
\(770\) | 28.8563 | + | 42.4821i | 1.03991 | + | 1.53095i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.884301 | − | 1.53165i | 0.0318267 | − | 0.0551255i | ||||
\(773\) | 7.14225 | − | 12.3707i | 0.256889 | − | 0.444944i | −0.708518 | − | 0.705693i | \(-0.750636\pi\) |
0.965407 | + | 0.260748i | \(0.0839693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8148 | + | 30.8561i | −0.639925 | + | 1.10838i | ||||
\(776\) | 6.54097 | + | 11.3293i | 0.234807 | + | 0.406698i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.03721 | − | 15.6529i | 0.324000 | − | 0.561184i | ||||
\(779\) | 3.61680 | − | 6.26448i | 0.129585 | − | 0.224448i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.52607 | + | 16.4996i | 0.340870 | + | 0.590403i | ||||
\(782\) | 0.670308 | + | 1.16101i | 0.0239702 | + | 0.0415176i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.92538 | − | 1.01936i | 0.247335 | − | 0.0364056i | ||||
\(785\) | −69.9449 | −2.49644 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.26997 | − | 5.66376i | 0.116562 | − | 0.201891i | −0.801841 | − | 0.597537i | \(-0.796146\pi\) |
0.918403 | + | 0.395646i | \(0.129479\pi\) | |||||||
\(788\) | −2.92757 | − | 5.07070i | −0.104290 | − | 0.180636i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.59248 | − | 14.8826i | 0.305707 | − | 0.529500i | ||||
\(791\) | 1.81081 | − | 3.74361i | 0.0643849 | − | 0.133108i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.1008 | − | 10.0922i | 0.997888 | − | 0.358383i | ||||
\(794\) | −1.20491 | − | 2.08696i | −0.0427606 | − | 0.0740635i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.96137 | − | 12.0575i | −0.246739 | − | 0.427365i | ||||
\(797\) | 24.2958 | + | 42.0815i | 0.860601 | + | 1.49060i | 0.871350 | + | 0.490662i | \(0.163245\pi\) |
−0.0107495 | + | 0.999942i | \(0.503422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.468383 | + | 0.811263i | 0.0165702 | + | 0.0287004i | ||||
\(800\) | −10.6045 | −0.374926 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.4622 | − | 21.5851i | 0.440055 | − | 0.762197i | ||||
\(803\) | 0.401858 | + | 0.696038i | 0.0141813 | + | 0.0245627i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −56.0058 | − | 82.4514i | −1.97395 | − | 2.90603i | ||||
\(806\) | −2.15452 | + | 11.9210i | −0.0758897 | + | 0.419898i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.38523 | 0.259812 | ||||||||
\(809\) | −41.7183 | −1.46674 | −0.733369 | − | 0.679831i | \(-0.762053\pi\) | ||||
−0.733369 | + | 0.679831i | \(0.762053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.40508 | 0.0844538 | 0.0422269 | − | 0.999108i | \(-0.486555\pi\) | ||||
0.0422269 | + | 0.999108i | \(0.486555\pi\) | |||||||
\(812\) | 1.45105 | − | 2.99986i | 0.0509219 | − | 0.105274i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.3619 | + | 47.3922i | −0.959034 | + | 1.66109i | ||||
\(815\) | 6.46146 | − | 11.1916i | 0.226335 | − | 0.392024i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.420518 | + | 0.728358i | 0.0147121 | + | 0.0254820i | ||||
\(818\) | −27.4769 | −0.960707 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.7773 | −1.28432 | ||||||||
\(821\) | −0.226645 | − | 0.392561i | −0.00790998 | − | 0.0137005i | 0.862043 | − | 0.506835i | \(-0.169185\pi\) |
−0.869953 | + | 0.493134i | \(0.835851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09531 | − | 3.62919i | 0.0730380 | − | 0.126506i | −0.827193 | − | 0.561917i | \(-0.810064\pi\) |
0.900231 | + | 0.435412i | \(0.143397\pi\) | |||||||
\(824\) | 1.99107 | − | 3.44863i | 0.0693621 | − | 0.120139i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.641059 | − | 0.943763i | −0.0223053 | − | 0.0328377i | ||||
\(827\) | −1.35282 | −0.0470421 | −0.0235211 | − | 0.999723i | \(-0.507488\pi\) | ||||
−0.0235211 | + | 0.999723i | \(0.507488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.2162 | −1.67462 | −0.837309 | − | 0.546730i | \(-0.815872\pi\) | ||||
−0.837309 | + | 0.546730i | \(0.815872\pi\) | |||||||
\(830\) | 41.5648 | 1.44273 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.39335 | + | 1.21869i | −0.117643 | + | 0.0422505i | ||||
\(833\) | 0.610851 | + | 0.771439i | 0.0211647 | + | 0.0267288i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4962 | − | 30.3044i | −0.605482 | − | 1.04873i | ||||
\(836\) | −1.90891 | + | 3.30633i | −0.0660210 | + | 0.114352i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.3331 | 0.356951 | ||||||||
\(839\) | −14.1093 | − | 24.4380i | −0.487107 | − | 0.843694i | 0.512783 | − | 0.858518i | \(-0.328614\pi\) |
−0.999890 | + | 0.0148244i | \(0.995281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.7068 | + | 23.7409i | 0.472649 | + | 0.818651i | ||||
\(842\) | −8.43511 | − | 14.6100i | −0.290693 | − | 0.503495i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.35399 | + | 5.80929i | 0.115449 | + | 0.199964i | ||||
\(845\) | −8.48514 | − | 50.6475i | −0.291898 | − | 1.74233i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.5419 | − | 28.7695i | −0.671468 | − | 0.988530i | ||||
\(848\) | −5.53204 | + | 9.58177i | −0.189971 | + | 0.329039i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.745346 | − | 1.29098i | −0.0255652 | − | 0.0442801i | ||||
\(851\) | 53.1053 | − | 91.9811i | 1.82043 | − | 3.15307i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.29308 | −0.112753 | −0.0563764 | − | 0.998410i | \(-0.517955\pi\) | ||||
−0.0563764 | + | 0.998410i | \(0.517955\pi\) | |||||||
\(854\) | −9.54044 | + | 19.7236i | −0.326467 | + | 0.674929i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.53679 | + | 6.12590i | 0.120885 | + | 0.209379i | ||||
\(857\) | −16.7918 | − | 29.0842i | −0.573596 | − | 0.993497i | −0.996193 | − | 0.0871794i | \(-0.972215\pi\) |
0.422597 | − | 0.906318i | \(-0.361119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6075 | + | 23.5688i | −0.464280 | + | 0.804157i | −0.999169 | − | 0.0407656i | \(-0.987020\pi\) |
0.534888 | + | 0.844923i | \(0.320354\pi\) | |||||||
\(860\) | 2.13801 | − | 3.70314i | 0.0729054 | − | 0.126276i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.1718 | − | 21.0822i | −0.414573 | − | 0.718061i | ||||
\(863\) | 7.05959 | − | 12.2276i | 0.240311 | − | 0.416231i | −0.720492 | − | 0.693463i | \(-0.756084\pi\) |
0.960803 | + | 0.277232i | \(0.0894172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.5276 | − | 51.1433i | 1.00397 | − | 1.73893i | ||||
\(866\) | −0.984059 | + | 1.70444i | −0.0334397 | + | 0.0579193i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.99483 | − | 7.35335i | −0.169536 | − | 0.249589i | ||||
\(869\) | −10.6883 | + | 18.5127i | −0.362576 | + | 0.628000i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.8128 | + | 9.98874i | −0.942402 | + | 0.338455i | ||||
\(872\) | 7.42350 | + | 12.8579i | 0.251391 | + | 0.435423i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.70491 | − | 6.41709i | 0.125320 | − | 0.217061i | ||||
\(875\) | 32.9127 | + | 48.4538i | 1.11265 | + | 1.63804i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.01911 | −0.270786 | −0.135393 | − | 0.990792i | \(-0.543230\pi\) | ||||
−0.135393 | + | 0.990792i | \(0.543230\pi\) | |||||||
\(878\) | 10.1318 | − | 17.5488i | 0.341931 | − | 0.592243i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.4107 | 0.654333 | ||||||||
\(881\) | −13.1358 | + | 22.7519i | −0.442558 | + | 0.766532i | −0.997878 | − | 0.0651039i | \(-0.979262\pi\) |
0.555321 | + | 0.831636i | \(0.312595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7341 | −0.630452 | −0.315226 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315226 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(884\) | −0.386865 | − | 0.327444i | −0.0130117 | − | 0.0110131i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.5415 | 0.958870 | ||||||||
\(887\) | −6.11884 | − | 10.5981i | −0.205450 | − | 0.355851i | 0.744826 | − | 0.667259i | \(-0.232533\pi\) |
−0.950276 | + | 0.311408i | \(0.899199\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.6434 | − | 2.09673i | 0.960667 | − | 0.0703222i | ||||
\(890\) | −2.11879 | − | 3.66986i | −0.0710221 | − | 0.123014i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.02744 | − | 1.77957i | −0.0344011 | − | 0.0595845i | ||||
\(893\) | 2.58883 | − | 4.48399i | 0.0866320 | − | 0.150051i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.8365 | − | 79.3911i | 1.53214 | − | 2.65375i | ||||
\(896\) | 1.15207 | − | 2.38175i | 0.0384879 | − | 0.0795687i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.1517 | − | 21.0474i | 0.405508 | − | 0.702360i | ||||
\(899\) | −4.23179 | −0.141138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.55529 | −0.0518143 | ||||||||
\(902\) | 45.7477 | 1.52323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.785895 | − | 1.36121i | −0.0261385 | − | 0.0452732i | ||||
\(905\) | 38.4395 | − | 66.5791i | 1.27777 | − | 2.21316i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.8899 | −0.760048 | −0.380024 | − | 0.924977i | \(-0.624084\pi\) | ||||
−0.380024 | + | 0.924977i | \(0.624084\pi\) | |||||||
\(908\) | −12.9149 | − | 22.3692i | −0.428595 | − | 0.742349i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.4638 | + | 22.1804i | 1.00986 | + | 0.735273i | ||||
\(911\) | −22.0074 | −0.729139 | −0.364570 | − | 0.931176i | \(-0.618784\pi\) | ||||
−0.364570 | + | 0.931176i | \(0.618784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.7029 | −1.71112 | ||||||||
\(914\) | −3.12651 | + | 5.41528i | −0.103416 | + | 0.179121i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.39496 | + | 9.34435i | 0.178255 | + | 0.308746i | ||||
\(917\) | −5.07553 | + | 0.371536i | −0.167609 | + | 0.0122692i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.9202 | 1.64672 | 0.823358 | − | 0.567522i | \(-0.192098\pi\) | ||||
0.823358 | + | 0.567522i | \(0.192098\pi\) | |||||||
\(920\) | −37.6732 | −1.24205 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.65625 | − | 16.7251i | 0.318012 | − | 0.550812i | ||||
\(923\) | 10.6707 | + | 9.03168i | 0.351229 | + | 0.297281i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.0502 | + | 102.278i | −1.94156 | + | 3.36288i | ||||
\(926\) | 10.7240 | + | 18.5745i | 0.352412 | + | 0.610396i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.629759 | − | 1.09077i | −0.0206729 | − | 0.0358064i | ||||
\(929\) | −9.00296 | −0.295377 | −0.147689 | − | 0.989034i | \(-0.547183\pi\) | ||||
−0.147689 | + | 0.989034i | \(0.547183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00449 | − | 5.05588i | 0.0656944 | − | 0.165700i | ||||
\(932\) | 1.92109 | + | 3.32742i | 0.0629274 | + | 0.108993i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.78510 | −0.156573 | ||||||||
\(935\) | 1.36429 | + | 2.36302i | 0.0446171 | + | 0.0772791i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.4359 | −1.38632 | −0.693159 | − | 0.720784i | \(-0.743782\pi\) | ||||
−0.693159 | + | 0.720784i | \(0.743782\pi\) | |||||||
\(938\) | 9.44267 | − | 19.5215i | 0.308314 | − | 0.637400i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.3244 | −0.858608 | ||||||||
\(941\) | 4.68568 | + | 8.11583i | 0.152749 | + | 0.264569i | 0.932237 | − | 0.361848i | \(-0.117854\pi\) |
−0.779488 | + | 0.626417i | \(0.784521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −88.7895 | −2.89138 | ||||||||
\(944\) | −0.431218 | −0.0140350 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.65950 | + | 4.60638i | −0.0864677 | + | 0.149766i | ||||
\(947\) | −18.1411 | − | 31.4213i | −0.589507 | − | 1.02106i | −0.994297 | − | 0.106646i | \(-0.965989\pi\) |
0.404790 | − | 0.914409i | \(-0.367344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.450143 | + | 0.381002i | 0.0146122 | + | 0.0123679i | ||||
\(950\) | −4.11966 | + | 7.13545i | −0.133659 | + | 0.231505i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.370925 | − | 0.0271522i | 0.0120217 | − | 0.000880008i | ||||
\(953\) | −9.41368 | − | 16.3050i | −0.304939 | − | 0.528170i | 0.672309 | − | 0.740271i | \(-0.265303\pi\) |
−0.977248 | + | 0.212101i | \(0.931969\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.8297 | − | 49.9345i | 0.932907 | − | 1.61584i | ||||
\(956\) | 5.12799 | − | 8.88194i | 0.165851 | − | 0.287262i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.85660 | + | 10.1439i | 0.189218 | + | 0.327735i | ||||
\(959\) | −41.9080 | + | 3.06772i | −1.35328 | + | 0.0990620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.85571 | − | 17.0706i | 0.317926 | − | 0.550664i | ||||
\(962\) | −7.14154 | + | 39.5142i | −0.230252 | + | 1.27399i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.316427 | + | 0.548068i | 0.0101914 | + | 0.0176521i | ||||
\(965\) | −3.49322 | + | 6.05043i | −0.112451 | + | 0.194770i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.63971 | −0.309992 | −0.154996 | − | 0.987915i | \(-0.549536\pi\) | ||||
−0.154996 | + | 0.987915i | \(0.549536\pi\) | |||||||
\(968\) | −13.1452 | −0.422502 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.8385 | − | 44.7536i | −0.829624 | − | 1.43695i | ||||
\(971\) | −18.2733 | −0.586419 | −0.293209 | − | 0.956048i | \(-0.594723\pi\) | ||||
−0.293209 | + | 0.956048i | \(0.594723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.78225 | − | 14.0214i | 0.217429 | − | 0.449506i | ||||
\(974\) | 25.7570 | 0.825308 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.14057 | + | 7.17168i | 0.132536 | + | 0.229560i | ||||
\(977\) | −32.0865 | −1.02654 | −0.513268 | − | 0.858228i | \(-0.671565\pi\) | ||||
−0.513268 | + | 0.858228i | \(0.671565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.63560 | + | 4.56499i | 0.0842340 | + | 0.145898i | ||||
\(980\) | −27.3570 | + | 4.02672i | −0.873888 | + | 0.128629i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.70024 | −0.149991 | ||||||||
\(983\) | 11.7559 | + | 20.3618i | 0.374955 | + | 0.649442i | 0.990320 | − | 0.138801i | \(-0.0443247\pi\) |
−0.615365 | + | 0.788242i | \(0.710991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5646 | + | 20.0306i | 0.368480 | + | 0.638226i | ||||
\(986\) | 0.0885262 | − | 0.153332i | 0.00281925 | − | 0.00488308i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.498231 | + | 2.75672i | −0.0158509 | + | 0.0877029i | ||||
\(989\) | 5.16168 | − | 8.94030i | 0.164132 | − | 0.284285i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1859 | 0.800058 | 0.400029 | − | 0.916503i | \(-0.369000\pi\) | ||||
0.400029 | + | 0.916503i | \(0.369000\pi\) | |||||||
\(992\) | −3.35985 | −0.106675 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.2310 | + | 0.748922i | −0.324507 | + | 0.0237544i | ||||
\(995\) | 27.4992 | + | 47.6300i | 0.871783 | + | 1.50997i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.49790 | + | 12.9867i | −0.237461 | + | 0.411294i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.722524 | + | 0.691346i | \(0.242982\pi\) | |||||||
\(998\) | 32.6494 | 1.03350 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.2.p.i.919.4 | 8 | ||
3.2 | odd | 2 | 546.2.k.b.373.1 | yes | 8 | ||
7.4 | even | 3 | 1638.2.m.g.1621.4 | 8 | |||
13.3 | even | 3 | 1638.2.m.g.289.4 | 8 | |||
21.11 | odd | 6 | 546.2.j.d.529.1 | yes | 8 | ||
39.29 | odd | 6 | 546.2.j.d.289.1 | ✓ | 8 | ||
91.81 | even | 3 | inner | 1638.2.p.i.991.4 | 8 | ||
273.263 | odd | 6 | 546.2.k.b.445.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.d.289.1 | ✓ | 8 | 39.29 | odd | 6 | ||
546.2.j.d.529.1 | yes | 8 | 21.11 | odd | 6 | ||
546.2.k.b.373.1 | yes | 8 | 3.2 | odd | 2 | ||
546.2.k.b.445.1 | yes | 8 | 273.263 | odd | 6 | ||
1638.2.m.g.289.4 | 8 | 13.3 | even | 3 | |||
1638.2.m.g.1621.4 | 8 | 7.4 | even | 3 | |||
1638.2.p.i.919.4 | 8 | 1.1 | even | 1 | trivial | ||
1638.2.p.i.991.4 | 8 | 91.81 | even | 3 | inner |